A minimal tight-binding model for ferromagnetic canted bilayer manganites

Half-metallicity in materials has been a subject of extensive research due to its potential for applications in spintronics. Ferromagnetic manganites have been seen as a good candidate, and aside from a small minority-spin pocket observed in La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ $(x=0.38)$, transport measurements show that ferromagnetic manganites essentially behave like half metals. Here we develop robust tight-binding models to describe the electronic band structure of the majority as well as minority spin states of ferromagnetic, spin-canted antiferromagnetic, and fully antiferromagnetic bilayer manganites. Both the bilayer coupling between the MnO$_2$ planes and the mixing of the $|x^2 - y^2>$ and $|3z^2 - r^2>$ Mn 3d orbitals play an important role in the subtle behavior of the bilayer splitting. Effects of $k_z$ dispersion are included.